Question

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 30 N acts on a certain object, the acceleration of the object is 10 (m)/(s^2). If the force is changed to 27 N, what will be the acceleration of the object?

Options:
A. 9 (m)/(s²)
B. 8 (m)/(s²)
C. 7 (m)/(s²)
D. 6 (m)/(s²)

Answer 1

The acceleration of the object when a force of 27 N is applied will be 9 m/s², according to Newton's second law and using direct variation.

Step-by-step explanation:

The question concerns the relationship between force, mass, and acceleration, and particularly how a change in force affects acceleration. This relationship is described by Newton's second law of motion, which states that force equals mass times acceleration (F=ma).

In the given scenario, a force of 30 N results in an acceleration of 10 m/s². Using the formula F=ma, we can determine the constant ratio of mass to force since the mass stays the same. To find the new acceleration when the force is changed to 27 N, we set up a proportion: 30/10 = 27/x, where x is the new acceleration. Solving for x gives us an acceleration of 9 m/s², matching option A.